Two students in a physics lab have to construct a constant-volume gas thermomete

Question

Two students in a physics lab have to construct a constant-volume gas thermometer as part of their end of year project. They use liquid nitrogen (-196°C) and boiling allyl alcohol (96.9°C) to calibrate the thermometer. The corresponding values of pressure are 0.250 atm and 1.450 atm. The students plot a pressure versus temperature graph with pressure on the y-axis and temperature on the x-axis.

(a) Determine the y intercept and slope of the linear graph that relates the pressure to the temperature.

(b) What value of absolute zero do the students get from this calibration? MUST BE IN C

Absolute zero corresponds to a pressure of zero for a gas maintained at constant volume.°C

(c) What pressure readings would this thermometer give for the freezing and boiling points of water?

Explanation / Answer

(a) Let the equation for the linear graph be P = mT + c

Then, the points (-196, 0.25) and (96.9, 1.450) satisfy the equation.

0.250 = -196m + c

1.450 = 96.9m + c

Eliminating 'c' from the above equations, we get,

1.450 = 96.9m + (0.250 + 196m)

=> 292.9m = 1.200

=> slope, m = 0.0041 atm/oC

y-intercept, c = 0.250 + (196 * 0.0041) = 1.054 atm

(b) At P = 0,

Taz = -c/m = -1.054/0.0041 = -257.07 oC

(c) Pressure reading for freezing point,

Pf = (0.0041 * 0) + 1.054 = 1.054 atm

Pressure reading for boiling point,

Pb = (0.0041 * 100) + 1.054 = 1.464 atm

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